Jeff, before you go out and buy a new lens, I highly recommend you stop by the Pro Digital Forum at dpreview. I can't speak for the other mods but I've not had experience photographing something as large as a rug from a birds eye view.
I do know that when photographing smaller items with perpendicular lines, you'll get that type of distortion when shooting at the widest angle of a zoom lens. You can minimize the effect by moving back and zooming in instead of standing close and shooting at wide angle. A focal length of about 50mm (35mm equivalent) works well. You can see a photo illustration of how effective the method is here:
http://www.digicamhelp.com/what-is-barrel-distortion/index.htmHowever, whether or not you can accomplish the same thing as easily with a 10x14" rug, I honestly don't know. As I said, ask around at dpreview. If you get an answer and have a moment to share it, please consider doing so. Sorry I can't be of more help.
http://forums.dpreview.com/forums/forum.asp?forum=1014